Question

4 Find the equation whose roots are the cubes of the roots of x+3x2+2 = 0.​

Answer 1

Given equation is x3 + 3x2 + 2 = 0

Put y = x3 so that x = y1/3

∴ y + 3y2/3 + 2 = 0

3y2/3 = – (y + 2)

Cubing on both sides, 27y2 = – (y + 2)3

= – (y3 + 6y2 + 12y + 8)

∴ y3 + 6y2 + 12y + 8 = 0

⇒ y3 + 33y2 + 12y + 8 = 0

Required equation is x3 + 33x2 +12x +8= 0

Answer 2

Answer:

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